The probability of failure modes for different types of resistors are listed in the Article, Resistor Reliability & Failure Mode Probability Distributions. Here I will summarize the causes for failure of different types resistors.

A fixed composition resistors normally fail to open circuit when overheated or overly stressed due to shock or vibration.

A variable composition resistor may wear out after extensive use, and worn away particles may cause high resistance short circuits.

Wirewound resistors may experience open windings due to overheating or stress

Wirewound resistors may experience the windings short circuited due to accumulation of dirt, dust, breakdown of the insulation coating or high humidity.

Film resistors fail to open circuit when overheated or overly stressed due to shock or vibration.

Film resistors also fails in its stability, due to changes in resistive material characteristics resulting in increase/decrease in resistance value.

For all types of resistors, Excessive humidity may cause an increase in resistance.

Potentiometers and presets fail to open circuit due to aging and/or heavy usage of resistance tracks.

Potentiometers and presets gives erratic output when the wiper and/or spindle fail due to excessive usage.

To learn more about designing for high reliability, you can read my previous article, Resistor Guidelines – Design For Reliability (DFR).